Mutagen will never cross the threshold, though it can take you up to it. Anything mutagen alone gives you can be gained even after you cross a threshold. Serum is the only way to breach a threshold, and you start having dreams about a given mutation path when you have enough mutations of that type to breach the threshold. Before you start having dreams, serum will just act as a more powerful mutagen.
Once you cross a threshold, you cannot go back or cross another threshold, though you can still use mutagen/serum to get the pre-threshold mutations from other branches.
Purifier randomly selects mutations and removes or downgrades them, no control over what it selects. Some post-threshold mutations cannot be purified, and thresholds themselves cannot be purified either. Purifier serum is just a more potent form, so it makes more random selections to remove.
So if you take medical mutagen until you have the dreams for it, then take medical serum you will cross the medical threshold. After that, you could take a thousand bird serum and you would still be a medical threshold mutant, but with lots of pre-threshold bird mutations. It is recommended to go with the mutagen+serum of the threshold you want first, then fill in others, as some mutation paths share many mutations, so it can be difficult to get the exact category you want at times if you use multiple types of mutagen first.
I would advise getting to where you have at least five or so units of purifier sitting around just in case, as some negative mutations can be crippling, though medical isn’t as bad as some other routes, especially if you have access to various drugs, such as if you do lab raids or clear a hospital or some pharmacies. Personally I tend to build up large stockpiles of whatever mutagen I want to take and purifier, then purify away any negatives as I get them until I only have positives. Be warned however that this takes an incredible amount of time, effort, and purifier/mutagen combo due to it being random rather than chosen or based on last mutation.
